The statistical nature of the mer combination process results in a molecular weight distribution in the final polymer. This is represented in the diagram and two 'averages' are shown on the plot.

The number-average molecular weight is given by:
< M_n > = S_i x_i M_i where x_i is the fraction of chains formed with a molecular weight M_i .

The weight average molecular weight is given by:
< M_w > = S_i w_i M_i where w_i is the weight fraction of molecular chains of weight M_i .

From: Callister,
"Materials Science and Engineering,"
Wiley (1997)

Material properties such as the melting point and elastic modulus of the polymer are dependent upon the molecular weight. In general, the melting point increases as the molecular weight goes up. The molecular weight distribution also influences properties and a wide weight distribution gives more variable properties than a narrow distribution.